(1) Field of the Invention
The present invention relates to a high-speed dynamics computation for a link system wherein links are connected via joints, and particularly relates to a high-speed dynamics computation for a link system used preferably for a forward dynamics computation which computes a joint acceleration in the case of applying joint displacements, joint velocities and joint torques of the link system.
(2) Prior Art Statement
Generally, a forward dynamics computation of a rigid-body link system has been widely used for a chain analysis or a design of control system in off-line operation. In the forward dynamic computation mentioned above, it has been highly required that a model having multiple degrees of freedom is simulated at a speed sufficient for interactive actions according to a widening of robot application. Such forward dynamics computation of the rigid-body link system mentioned above is applied to a motion creation of humanoid robots or human figures based on the dynamics in addition to a dynamics simulation of robots. In each of these technical fields, it is utilized as a form of software with an external interface such as an input means for joint torques or a display means for calculation results.
As an example of the forward dynamics computation of the rigid-body link system mentioned above, the following literatures 1–3 have been known. Literature 1: Anderson, K. S. and Duan, S: “Highly Parallelizable Low Order Algorithm for the Dynamics of Complex Multi-Rigid-Body Systems”, AIAA Journal of Guidance, Control and Dynamics, 2000. Literature 2: Featherstone, R.: “A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n)) Calculation of Rigid-Body Dynamics”, International Journal of Robotics Research, vol. 18, no. 9, pp. 867–892, 1999. Literature 3: Fijany, A. Sharf, I. And D'Eleuterio, G. M. T.: “Parallel O(log N) Algorithms for Computation of Manipulator Forward Dynamics”, IEEE Transactions on Robotics and Automation, vol. 11, no. 8, pp. 389–400, 1995.
In the techniques described on the literatures 1–3 mentioned above, all of them intend to perform the forward dynamics computation faster by parallel computations. If the number of the links is N, a computation time becomes O(logN) by utilizing O(N) processors. However, there are following drawbacks in these techniques. That is, in the literature 1, since approximate values are obtained by a convergent calculation, accurate values cannot be obtained. In the literature 2, algorithms for serial and parallel computations are largely different from each other. In the literature 3, it is difficult to apply this technique to complex chains such as closed kinematic chains.